I'm very eager to purchase a GX Typhoon for my HTPC running Windows 7 64-bit, but from everything I've read both here and the forums at lcdstudio.com I've been unable to discern whether this device will work at all with 7MC, allow me to display the name of the currently playing recording and its progress, etc.

Yes, the GX and LCDStudio does work with Windows 7 Media Centre to display track information such as title, artist, and position. I created a quick demo screen and added the screenshot below to clear up any confusion.